Sensorless enhancement of an atomic force microscope micro-cantileverquality factor using piezoelectric shunt controlM. Fairbairn and S. O. R. Moheimani Citation: Rev. Sci. Instrum. 84, 053706 (2013); doi: 10.1063/1.4805108 View online: http://dx.doi.org/10.1063/1.4805108 View Table of Contents: http://rsi.aip.org/resource/1/RSINAK/v84/i5 Published by the AIP Publishing LLC. Additional information on Rev. Sci. Instrum.Journal Homepage: http://rsi.aip.org Journal Information: http://rsi.aip.org/about/about_the_journal Top downloads: http://rsi.aip.org/features/most_downloaded Information for Authors: http://rsi.aip.org/authors

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REVIEW OF SCIENTIFIC INSTRUMENTS 84, 053706 (2013)

Sensorless enhancement of an atomic force microscope micro-cantileverquality factor using piezoelectric shunt control

M. Fairbairna) and S. O. R. Moheimanib)

School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan,NSW 2308, Australia

(Received 10 January 2013; accepted 1 May 2013; published online 23 May 2013)

The image quality and resolution of the Atomic Force Microscope (AFM) operating in tapping modeis dependent on the quality (Q) factor of the sensing micro-cantilever. Increasing the cantilever Qfactor improves image resolution and reduces the risk of sample and cantilever damage. Active piezo-electric shunt control is introduced in this work as a new technique for modifying the Q factor of apiezoelectric self-actuating AFM micro-cantilever. An active impedance is placed in series with thetip oscillation voltage source to modify the mechanical dynamics of the cantilever. The benefit ofusing this control technique is that it removes the optical displacement sensor from the Q controlfeedback loop to reduce measurement noise in the loop and allows for a reduction in instrument size.© 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4805108]

I. INTRODUCTION

The Atomic Force Microscope (AFM)1 obtains three-dimensional images of sample surfaces through measurementof the interatomic forces between a sharp probe tip, located atthe end of a micro-cantilever, and the sample surface. Whenoperating in tapping mode2 the cantilever tip is oscillated ator close to its first resonance frequency, lightly touching thesample once every oscillation cycle. A schematic showing thetypical instrumentation of an AFM operating in tapping modeis shown in Fig. 1.

The sample is placed on a piezoelectric scanner whichscans the sample in a raster pattern below the cantilever. Asthe sample is scanned below the cantilever the cantilever tiposcillation amplitude A(t) varies in proportion to the sampletopography. Cantilever deflection is measured optically.3, 4

A feedback controller regulates the vertical position ofthe sample, maintaining A(t) at a set-point value Aset. As thesample topography is an input disturbance to this feedbackloop the output of the controller is proportional to variationsin the sample topography. A three-dimensional image of thesample is obtained by plotting the control signal as a functionof the lateral scan position.

The variation in A(t) as a result of a change in sampleheight is dependent on the cantilever Q factor. A high Q fac-tor cantilever produces a larger change in A(t) than a low Qfactor cantilever. The high Q factor cantilever, therefore, has ahigher force sensitivity5–7 providing better image resolution.For samples which have very fine features it is beneficial touse a high Q factor cantilever for high resolution images. Bi-ological samples are commonly imaged in a liquid environ-ment. Hydrodynamic forces cause a significant reduction ofthe cantilever Q factor8, 9 when imaging in liquid. This reduc-tion in cantilever Q factor reduces the force sensitivity of thecantilever considerably.

a)Electronic mail: Matthew.Fairbairn@newcastle.edu.aub)Electronic mail: Reza.Moheimani@newcastle.edu.au

It is important to minimize tip-sample forces in order tominimize tip/sample damage and deformation of soft sam-ples. The tip-sample force is inversely proportional to the can-tilever Q factor.9, 10 The reduction in sample deformation, as aresult of increasing the cantilever Q factor, has been demon-strated by several authors.11–13

The cantilever Q factor may be modified by feedback ofthe cantilever tip velocity.14 This is termed active Q control.It is difficult and relatively expensive to incorporate a velocitysensor into the AFM. Therefore, it is necessary to estimate tipvelocity from the displacement signal. Differentiation of thedisplacement signal is not recommended as high frequencynoise is amplified in the feedback loop. Tip velocity is com-monly estimated by delaying the displacement signal by 3π

2radians at the tip oscillation frequency. A gain is then appliedto this signal and subtracted from the probe oscillation signalto obtain the desired cantilever Q factor.

One drawback of using the time delay method of veloc-ity estimation is that spill-over effects from the control actionmay affect higher order modes of the cantilever, leading topossible degradation of system performance.15

The feedback signal used for most implementations ofactive Q control relies on the displacement signal obtainedfrom the optical sensor. The optical deflection sensing tech-nique used to measure cantilever tip displacement in com-mercial AFMs introduces a significant amount of noise intothe deflection measurement. In addition to electronic noise,two other forms of noise are introduced by the optical sen-sor. The first form of noise introduced by the optical sensor isdue to stray beams of light reflecting off the sample surfaceand back into the sensor.16 The second form of noise is due tolight reflecting back from the cantilever and the sample intothe laser source.16 Imaging in a liquid environment is partic-ularly problematic due to reflection and refraction of the laserbeam at the interface between air and water.

Other problems with the optical deflection sensing tech-nique include the time taken to align the laser beam and thesize of the sensor. The task of aligning the laser beam must be

0034-6748/2013/84(5)/053706/8/$30.00 © 2013 AIP Publishing LLC84, 053706-1

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053706-2 M. Fairbairn and S. O. R. Moheimani Rev. Sci. Instrum. 84, 053706 (2013)

FIG. 1. Tapping mode AFM instrumentation.

completed every time that the cantilever is changed. This canbe a tedious and time consuming task. The optical sensor oc-cupies a relatively large amount of space. Reducing the sizeof the sensor is an advantage for applications which use anarray of cantilevers17–19 and to reduce the size of the AFM.18

The technique of active piezoelectric shunt control, in-troduced in this work to modify the effective Q factor ofa piezoelectric self-actuated AFM micro-cantilever, removesthe optical sensor from the Q control feedback loop. If thecantilever displacement can be measured with the piezoelec-tric transducer20–22 it would be possible to remove the opticalsensor from the AFM altogether, overcoming the limitationsof the optical sensing technique mentioned above.

II. ACTIVE PIEZOELECTRIC SHUNT CONTROL

Passive piezoelectric shunt control23 is a popular methodof controlling vibration in structures such as spacecraft24 andaircraft components.25 A piezoelectric transducer is bonded tothe surface of the structure with a passive electrical impedanceconnected to its electrodes. The piezoelectric transducer con-verts the mechanical energy of the structure to electrical en-ergy and vice versa. The dynamics of the electrical circuithave a strong influence on the mechanical dynamics of thestructure.

Fairbairn et al.26 reduced the Q factor of a piezoelec-trically actuated AFM micro-cantilever using passive piezo-electric shunt control. A synthetic impedance emulating aninductance and a resistance was placed in series with the can-tilever oscillation voltage source to create an LRC circuit.This LRC circuit was tuned to the mechanical resonance ofthe cantilever to ensure that the electrical dynamics of thecircuit had maximum influence over the mechanical dynam-ics of the cantilever. By tuning the resistance in the circuit areduction in the cantilever Q factor from 297.6 to 35.5 wasachieved.

Passive piezoelectric shunt control cannot be used in ap-plications where an increase in the cantilever Q factor is re-quired to increase force sensitivity and reduce tapping forces.To increase the cantilever Q factor using piezoelectric shunt

control, energy must be added to the system. This requiresthe design of an active impedance in the piezoelectric shuntcontrol framework.

The concept of using active piezoelectric shunt control toincrease the Q factor of a cantilever has recently been demon-strated by Zhao et al.27 Their experiments were conducted ona large cantilever (0.043 m × 0.433 m) with a resonance fre-quency of 91.7 Hz. An inductance and a negative resistancewere connected to the terminals of a piezoelectric transducerwhich was bonded to the cantilever surface. To test the influ-ence of the electrical impedance on the cantilever dynamics aseparate piezoelectric transducer bonded to the cantilever wasused for actuation.

In this work the technique of active piezoelectric shuntcontrol is applied to a piezoelectric AFM micro-cantileverwith a resonance frequency of approximately 50 kHz. Thepiezoelectric layer on the surface of the cantilever is used tosimultaneously oscillate the cantilever and modify its dynam-ics in a way that enhances the Q factor.

A. Piezoelectric transducer electrical model

The AFM micro-cantilever chosen to demonstrate theconcept of active piezoelectric shunt control in this work isthe DMASP micro-cantilever manufactured by Bruker.28 Thisdevice consists of a silicon cantilever which has a length of120 μm and a width of 55 μm with a thin layer of piezo-electric zinc-oxide (ZnO) material deposited on the bottomsurface. A probe tip which has a height of 15–20 μm and atip radius of approximately 10 nm is found on the undersideof the cantilever. A layer of titanium gold (Ti/Au) is bondedabove and below the ZnO layer acting as electrodes. Apply-ing a voltage to the electrodes causes the piezoelectric layer toexpand or contract, depending on the polarity of the voltage,resulting in flexure of the cantilever. A sinusoidal voltage isapplied to the electrodes to oscillate the cantilever tip whenoperating in tapping mode.

In the design of piezoelectric shunt control systems thepiezoelectric transducer is commonly modeled electrically asa strain dependent voltage source vp in series with a capaci-tance Cp.23 This model was used to design the passive piezo-electric shunt control system used for reduction of the can-tilever Q factor in Ref. 26.

Initial experiments with active piezoelectric shunt con-trol of the DMASP micro-cantilever for Q factor enhance-ment indicated that the vp in series with Cp model does notwork well for this application. The experimental results didnot match the values calculated for the shunt impedance pa-rameters. This issue was also observed by Zhao et al.27 intheir experimental work. Zhao et al.27 concluded that the mis-match between expected results and experimental results wasdue to frequency dependent electrical energy losses (dielectriclosses) which may be modeled as a resistance Rp in parallelwith Cp and vp.

The frequency response of the DMASP micro-cantileverelectrical impedance was measured in Refs. 29–31. Signifi-cant electrical energy losses in the ZnO piezoelectric trans-ducer were observed.

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053706-3 M. Fairbairn and S. O. R. Moheimani Rev. Sci. Instrum. 84, 053706 (2013)

When the cantilever is modeled electrically as a resis-tance Rp in parallel with Cp and vp the transfer function froma voltage v(s) applied to the transducer terminals to the chargeq(s) generated at the terminals is represented by

Gqv(s) = q(s)

v(s)= αCpGdv(s) + Cp + 1

Rps, (1)

where Gdv is the transfer function from v(s) to the cantilevertip displacement d(s) and is given by

Gdv(s) = d(s)

v(s)= βvω

2n

s2 + ωn

Qs + ω2

n

. (2)

Here ωn is the natural frequency of the cantilever, βv is thesteady state gain of Gdv , and α is the piezoelectric voltage-displacement coefficient (α = vp

d).

The impedance of the piezoelectric transducer may nowbe derived as

Zp(s) = v(s)

i(s)= v(s)

sq(s)

= 1

sGqv(s)= 1

αCpGdv(s)s + Cps + 1Rp

. (3)

The values for Cp and Rp were measured using an AgilentE4980A LCR meter. Cp was measured to be 28.5 pF and Rp

was found to be 6.7 M�.The frequency response of Gdv(s) was obtained by ap-

plying a pseudo random signal to the cantilever electrodesand measuring the resulting tip displacement with a Micro-scope Scanning Laser Doppler Vibrometer (Polytec MSV400). The frequency response of Gdv(s) is shown in Fig. 2.The mathematical model of Gdv(s) obtained by systemidentification is

Gdv(s) = 2126

s2 + 1472s + 1.119 × 1011(4)

and is also shown in Fig. 2.A frequency response of the cantilever impedance, shown

in Fig. 3, was obtained by measuring the voltage appear-ing across its electrodes in response to the application of aswept sine current. The transfer function obtained from this

FIG. 2. DMASP micro-cantilever frequency response (- -) and fittedmodel (—).

FIG. 3. Frequency response of the DMASP micro-cantilever electricalimpedance.

frequency response is

Zp(s) = s2 + 1472s + 1.119 × 1011

2.85 × 1011s3 + 1.912 × 107s2 + 3.191s + 16700.

(5)

By equating (3) and (5) the value of α was found to beapproximately 4 × 104 V/m.

B. Electromechanical model of the piezoelectricshunt system

A schematic of the micro-cantilever with the attachedshunt circuit is shown in Fig. 4. The piezoelectric shunt con-trol system may be modeled by the block diagram of Fig. 5.In this representation the cantilever is modeled as the systemG. The cantilever has two inputs: the terminal voltage v anda disturbance strain w. This disturbance strain is a result ofvariations in the sample topography when scanning. The can-tilever’s two outputs are the tip displacement d and the chargegenerated at its terminals q. vs is the voltage applied to the cir-cuit and vz is the voltage appearing across the terminals of theshunt impedance. The initial tip displacement due to a distur-bance is represented by dw. The transfer function from w(s)to dw(s) is

Gdww(s) = dw(s)

w(s)= βwω2

n

s2 + ωn

Qs + ω2

n

, (6)

where βw is the steady state gain of Gdww(s).

FIG. 4. Piezoelectric AFM micro-cantilever with attached shunt circuit.

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053706-4 M. Fairbairn and S. O. R. Moheimani Rev. Sci. Instrum. 84, 053706 (2013)

FIG. 5. Block diagram of the piezoelectric shunt control system.

C. Modelling the transfer function from actuatingvoltage to tip displacement

From the block diagram of Fig. 5 the transfer functionfrom vs to v may be derived as

Gvvs(s) = v(s)

vs(s)= 1

1 + sZ(s)Gqv(s). (7)

Substituting (1) into (7) gives

Gvvs(s) =

1

1+sZ(s)(Cp+ 1

Rps

)1 + sZ(s)CpαGdv(s)

1+sZ(s)(Cp+ 1

Rps

) . (8)

Let

H (s) = 1

1 + sZ(s)(Cp + 1

Rps

) (9)

and

K(s) = sZ(s)Cpα

1 + sZ(s)(Cp + 1

Rps

) , (10)

then

Gvvs(s) = H (s)

1 + K(s)Gdv(s). (11)

The transfer function from vs to d, when the shunt impedanceis connected, is now found to be

Gdvs(s) = Gvvs

(s)Gdv(s) = H (s)Gdv(s)

1 + K(s)Gdv(s). (12)

Gdvsmay be viewed as a negative feedback loop with a filter

H(s) in the feed forward path.When imaging in tapping mode the oscillation voltage is

a sinusoidal signal. The filter H(s) results in a modification inthe magnitude and phase of this signal. The modification ofphase does not affect the performance of the device and themodification in the magnitude may be accommodated for byvarying the amplitude of the input signal.

D. Modelling the transfer function from sampletopography to tip displacement

To obtain the transfer function from w(s) to d(s), vs(s) isfirst set to zero. From Fig. 5 it is observed that

v(s) = −vz(s) (13)

and

vz(s) = sq(s)Z(s), (14)

where q(s) is given by

q(s) = −vz(s)Cp − vz(s)αCpGdv(s) − vz(s)

Rps+ dw(s)αCp.

(15)Substituting (15) into (14) gives

vz(s) = (−vz(s)Cp − vz(s)αCpGdv(s)

− vz(s)

Rps+ dw(s)αCp)sZ(s). (16)

Substituting (13) into (16) results in the transfer function

Gvdw(s) = v(s)

dw(s)

= −αsZ(s)Cp

1 + sZ(s)(Cp + 1

Rps

)+ αsZ(s)CpGdv(s)

. (17)

From Fig. 5 it is observed that

d(s) = Gvdw(s)Gdv(s)dw(s) + dw(s). (18)

Substituting (17) into (18) results in the transfer function

Gddw(s) = d(s)

dw(s)= 1

1 + αsZ(s)CpGdv(s)

1+sZ(s)(Cp+ 1

Rps

)

= 1

1 + K(s)Gdv(s). (19)

Combining (19) and (6) results in the transfer function

Gdw(s) = Gddw(s)Gdww(s)

= Gdww(s)

1 + K(s)Gdv(s). (20)

Gdww(s) has the same poles as Gdv(s), the only difference be-ing the steady state gain βw. The transfer function Gdw(s) maybe written as

Gdw(s) = λGdv(s)

1 + K(s)Gdv(s), (21)

where λ = βw

βv. In the above form Gdw(s) may be viewed as a

negative feedback loop, as shown in Fig. 6. The closed looppoles may be placed in the s plane to obtain the desired Qfactor by design of the feedback controller K(s).

Note that the transfer function of the controller K(s),when an impedance Z(s) = Ls − R is applied, is a filter witha phase lag of π

2 at the filters resonance frequency fr. If fr istuned to the oscillation frequency of the cantilever the con-troller is effectively estimating the cantilever tip velocity andapplying a negative gain. The gain and bandwidth of controlmay be tuned by varying the parameters R and L.

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053706-5 M. Fairbairn and S. O. R. Moheimani Rev. Sci. Instrum. 84, 053706 (2013)

FIG. 6. Feedback interpretation of the transfer function from a disturbancew to tip displacement d.

III. SYNTHETIC IMPEDANCE

An active impedance such as Ls − R cannot be im-plemented using passive components. Cantilever parameters,such as Cp and α, will vary with material imperfections andmanufacturing tolerances. Environmental conditions such ashumidity, temperature, and air pressure will cause variationsin the cantilever resonance frequency. The values of R andL required to obtain a desired cantilever Q factor will, there-fore, vary from cantilever to cantilever and with environmen-tal conditions. A synthetic impedance was designed to imple-ment the active impedance and to allow for fine tuning of thevalues of R and L.

To implement an arbitrary impedance Z(s) synthetically32

the terminal voltage vz(s) is measured and a current sourceapplies an appropriate current to mimic the voltage to cur-rent relationship of the impedance (Z(s) = vz(s)

iz(s) ). The cur-rent supplied by the current source is iz(s) = vz(s)Y (s), whereY (s) = 1

Z(s) .The circuit of Fig. 7, which shows the piezoelectric

micro-cantilever attached to a synthetic impedance, is equiv-alent to the shunt impedance circuit shown in Fig. 4 if

FY (s) = R

Y (s)= R

Ls − R. (22)

FIG. 7. Piezoelectric shunt control circuit implemented with a syntheticimpedance.

FIG. 8. Admittance filter FY(s).

From Fig. 7 it is observed that

vout (s)

vz(s)= FY (s) = R

Ls − R(23)

and

iz(s) = vout (s)

R. (24)

The resulting impedance is now found to be

Z(s) = vz(s)

iz(s)= vz(s)R

vout (s)= Ls − R. (25)

A block diagram implementation of FY(s) is shown inFig. 8. By varying R and the gain (R

L) of the integrator in the

filter FY(s) the values of L and R may be modified accordingly.The admittance filter FY(s) is implemented with oper-

ational amplifiers in the schematic of Fig. 9 which showsthe piezoelectric micro-cantilever attached to the syntheticimpedance. The non-inverting summer, shown in Fig. 7,which adds the oscillation voltage vs to the cantilever termi-nal voltage is incorporated into the admittance filter circuitto reduce the number of operational amplifiers required inthe circuit. The operational amplifiers used in this circuit areLinear Technology LT1468 operational amplifiers.33 In thisimplementation the value of the inductance is determined byL = RRIC.

When increasing the cantilever Q factor the poles of thecantilever are pushed toward the jω axis of the complex plane.As the poles are shifted toward the jω axis the risk of the can-tilever becoming unstable is increased. Cantilever instabilitymay result in damage to the cantilever and/or sample. Themaximum amplitude at which the cantilever can oscillate, ifthe system goes unstable, may be controlled by limiting thepower supply voltage of the operational amplifier to which thecantilever is connected, in Fig. 9. This may avoid any damagewhich might occur if the system does become unstable.

IV. EXPERIMENTAL DEMONSTRATION

A. Determination of shunt impedance parameters

1. Inductance

For the electrical dynamics to have a sufficient influenceon the mechanical dynamics of the cantilever the resonancefrequency fe created by the electrical circuit must be tunedclose to the mechanical resonance fr of the cantilever. Theinductance tuning ratio is defined as

δ = fe

fr

. (26)

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053706-6 M. Fairbairn and S. O. R. Moheimani Rev. Sci. Instrum. 84, 053706 (2013)

FIG. 9. Piezoelectric shunt control circuit implemented with a synthetic impedance. In this schematic the admittance filter FY(s) is implemented with operationalamplifiers.

For the piezoelectric shunt control circuit shown inFig. 4 fe is given by

fe = 1

2π

√1

LCp

− 1

(RpCp)2. (27)

The necessary inductance may be found by tuning δ closeto 1. For an initial demonstration of the active piezoelectricshunt control technique this was achieved by setting fe = fr(δ = 1). fr was measured from the frequency response shownin Fig. 2 to be 53234 Hz, therefore fe was be tuned to53234 Hz. The necessary inductance is calculated by substi-tuting the values for fe, Cp, and Rp into (27). The value for Lwas found to be 313.56 mH.

2. Resistance

The characteristic equation (ACL) of Gdw(s) is1 + K(s)Gdv . A root locus of Gdw(s) was obtained byrearranging ACL into the form

ACL = 1 + R(ψs3 + ψ2ζωrs

2 + ψω2r s + Cpαβvω

2r s)

Lψs4 + Lψ2ζωrs3 + γ s2 + 2ζωrs + ω2r

,

(28)where ψ = Cp + 1

Rpsand γ = 1 + Lψω2

r + LCpαβvω2r .

The root locus when δ is tuned to 1, for R ∈ [−∞, 0], isshown in Fig. 10. A zoomed in view of the upper left quadrantof the root locus is shown in Fig. 11. As R is reduced, the polesof Gdw(s) shift toward the right of the complex plane, increas-ing the Q factor of the cantilever. The cantilever reaches apoint of instability when the poles cross the imaginary axis.The value of R, which causes the system to go unstable, is de-termined by conducting a Routh-Hurwitz stability analysis on

ACL. The value of R which causes system instability, when δ istuned to 1, is −3250 �. A slightly higher value of resistance(−3150 �) was chosen for this initial test to ensure stabilityof the cantilever.

B. Cantilever frequency response

The force sensitivity and tip-sample force of the AFMoperating in tapping mode are dependent on the dynamicsof Gdw(s). To measure the frequency response of Gdw(s)a piezoelectric actuator is placed underneath the cantilevermounting base with an excitation signal applied to the actu-ator. Difficulties were encountered with this method due to

FIG. 10. Root locus of Gdw(s) when δ = 1. A zoomed in view of the sectioninside the red square is shown in Fig. 11.

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053706-7 M. Fairbairn and S. O. R. Moheimani Rev. Sci. Instrum. 84, 053706 (2013)

FIG. 11. Upper left quadrant of the root locus of Gdw(s) when δ = 1(R ∈ [ − ∞, 0]).

the additional dynamics added to the system by the cantilevermounting base and the piezoelectric actuator.

An alternative method of measuring the frequency re-sponse of Gdw(s), when the active piezoelectric shunt con-troller is implemented, is to apply a filtered excitation signalto the cantilever electrodes. Equating (12) and (21) gives

Gdw(s) = λH−1(s)Gdvs(s). (29)

Gdw(s) is therefore equivalent to H−1(s)Gdvs(s) multiplied by

a gain λ. The poles of the system are not affected by the gainλ. λ may therefore be disregarded and the frequency responseof H−1(s)Gdvs

(s) used to determine the Q factor of Gdw(s).The filter H−1(s) is non-causal. H−1(s) may be approximatedphysically by adding fast poles into the transfer function. Theapproach taken in this work was to obtain the frequency re-sponse of H−1(s)Gdvs

(s) by filtering the frequency responseof Gdvs

(s) with H−1(s) afterward using MATLAB.An active shunt impedance containing a negative resis-

tance of −3150 � and an inductance of 313.56 mH wasapplied to the DMASP micro-cantilever. The frequency re-sponse plot of H−1(s)Gdvs

(s) for this system is shown inFig. 12. The Q factor of the left resonance peak was mea-sured to be 2165 with the right peak having a Q factor of767. The cantilever Q factor with no applied shunt impedancewas measured to be 178. Using the left resonance peak of theshunt controlled cantilever for tapping mode imaging wouldresult in an increase of the effective cantilever Q factor by over12 times.

FIG. 12. Frequency response of Gdvs (s) with no active piezoelectric shuntcontrol (- -) and H−1(s)Gdvs (s) with a shunt impedance consisting of aninductance of 313.56 mH and a negative resistance of −3150 � (—).

FIG. 13. Frequency response of Gdvs (s) with no active piezoelectric shuntcontrol (- -) and H−1(s)Gdvs (s) with a shunt impedance consisting of aninductance of 306.10 mH and a negative resistance of −2450 � (—).

V. AFM IMAGING WITH THE ACTIVE PIEZOELECTRICSHUNT CONTROL TECHNIQUE

To test the efficacy of the active piezoelectric shunt con-troller images of a sample with fine features were acquiredwith an NT-MDT NTEGRA AFM.34 The sample chosento demonstrate this technique consisted of clusters of goldnanoparticles sputtered on a silicon wafer, which is commer-cially available from Nanosurf Instruments.35 The featuresfound on this sample were less than 6 nm high which is idealfor testing the effect of increasing the cantilever Q factor onimage quality.

A 350 nm × 350 nm section of the sample was scannedwith no cantilever Q factor enhancement at a scan speed of1 μm/s. The image obtained is shown in Fig. 14(a). The ac-tive piezoelectric shunt controller was then placed in the tiposcillation circuit and the cantilever Q factor tuned by vary-ing L and R. The amount of Q enhancement required to im-prove the quality of the image was determined experimentally.Through trial and error it was found that a Q factor of 410gave the greatest improvement in image quality. Increasingthe Q factor further leads to significant oscillations appearingin the image due to low Z axis feedback loop stability mar-gins. The shunt impedance parameters of L = 306.10 mH andR = −2450 � were required to increase the cantilever Q fac-tor from 178 to 410. A frequency response of Gdvs

(s) withactive piezoelectric shunt control and H−1(s)Gdvs

(s) with the

FIG. 14. Images of the gold cluster sample obtained at a scan speed of1 μm/s with and without enhancement of the cantilever Q factor. The scanarea is 350 nm × 350 nm. (a) Q factor 178, no shunt control. (b) Q factor410, with shunt control.

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053706-8 M. Fairbairn and S. O. R. Moheimani Rev. Sci. Instrum. 84, 053706 (2013)

shunt impedance is shown in Fig. 13. The resonance peak onthe left was used for imaging. The image obtained is shownin Fig. 14(b).

Comparing the images of Figs. 14(a) and 14(b) it can beseen that the sample features in the image obtained using ac-tive piezoelectric shunt control to enhance the cantilever Qfactor are higher, giving a sharper image contrast.

VI. CONCLUSION

The benefits of using a high Q factor cantilever whenimaging in tapping mode AFM have been highlighted in thisarticle. The increased force sensitivity and reduced tip-sampleforce as a result of increasing the cantilever Q factor are ben-eficial in many imaging applications such as imaging sam-ples with fine features, soft samples, and samples in a fluidenvironment.

Active piezoelectric shunt control was introduced in thiswork as a new technique of increasing the Q factor of a piezo-electrically actuated AFM micro-cantilever. This method of Qcontrol has an advantage over existing Q control techniquesin that it removes the optical sensor from the Q control feed-back loop, reducing measurement noise in the loop. If thismethod of active Q control is used in conjunction with al-ternative methods of measuring the cantilever displacementwhich work by measuring the current through the piezoelec-tric transducer bonded to the cantilever, the optical sensor maybe removed from the instrument altogether. Removing the op-tical sensor is not only an advantage for reducing sensor noise,it allows for a reduction in the size of the AFM which is a ben-efit in many applications. The compact size and low cost ofthe active piezoelectric shunt control instrumentation enablesthe active piezoelectric shunt controller to be easily integratedinto existing AFMs.

A high cantilever Q factor is desired in many other can-tilever sensing applications such as measuring air pressure,30

temperature,36 humidity,37 and the concentration of chemicaland biological substances.38–40 The above mentioned benefitsof active piezoelectric shunt control are also desirable in theseapplications.

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